TY - GEN

T1 - On the Structure of Two-Layer Cellular Neural Networks

AU - Ban, Jung Chao

AU - Chang, Chih Hung

AU - Lin, Song-Sun

PY - 2013

Y1 - 2013

N2 - Let Y⊆{-1,1}ℤ∞×2 be the mosaic solution space of a two-layer cellular neural network (TCNN). We decouple Y into two subspaces, say Y(1) and Y(2), and give a necessary and sufficient condition for the existence of factor maps between them. In such a case, Y(i) is a sofic shift for i = 1,2. This investigation is equivalent to study the existence of factor maps between two sofic shifts. Moreover, we investigate whether Y(1) and Y(2) are topological conjugate, strongly shift equivalent, shift equivalent, or finitely equivalent via the well-developed theory in symbolic dynamical systems. This clarifies, in a TCNN, each layer's structure.

AB - Let Y⊆{-1,1}ℤ∞×2 be the mosaic solution space of a two-layer cellular neural network (TCNN). We decouple Y into two subspaces, say Y(1) and Y(2), and give a necessary and sufficient condition for the existence of factor maps between them. In such a case, Y(i) is a sofic shift for i = 1,2. This investigation is equivalent to study the existence of factor maps between two sofic shifts. Moreover, we investigate whether Y(1) and Y(2) are topological conjugate, strongly shift equivalent, shift equivalent, or finitely equivalent via the well-developed theory in symbolic dynamical systems. This clarifies, in a TCNN, each layer's structure.

UR - http://www.scopus.com/inward/record.url?scp=84893545209&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-7333-6_20

DO - 10.1007/978-1-4614-7333-6_20

M3 - Conference contribution

AN - SCOPUS:84893545209

SN - 9781461473329

T3 - Springer Proceedings in Mathematics and Statistics

SP - 265

EP - 273

BT - Differential and Difference Equations with Applications - Contributions from the International Conference on Differential and Difference Equations and Applications

PB - Springer New York LLC

T2 - International Conference on Differential and Difference Equations and Applications

Y2 - 4 July 2011 through 8 July 2011

ER -